Filter Function Formalism and Software Package to Compute Quantum Processes of Gate Sequences for Classical Non-Markovian Noise

TL;DR

This paper extends the filter function formalism to describe quantum processes under classical non-Markovian noise, providing exact results, a composition rule, and an open-source Python package for analyzing quantum gate sequences affected by such noise.

Contribution

It introduces a novel application of the filter function formalism to unital quantum operations and provides a software package for practical computations.

Findings

Exact results for quantum processes under non-Markovian noise

A simple composition rule for sequences of quantum operations

Open-source Python package for noise-averaged transfer matrix calculations

Abstract

Correlated, non-Markovian noise is present in many solid-state systems employed as hosts for quantum information technologies, significantly complicating the realistic theoretical description of these systems. In this regime, the effects of noise on sequences of quantum gates cannot be described by concatenating isolated quantum operations if the environmental correlation times are on the scale of the typical gate durations. The filter function formalism has been successful in characterizing the decay of coherence under the influence of such classical, non-Markovian environments and here we show it can be applied to describe unital evolution within the quantum operations formalism. We find exact results for the quantum process and a simple composition rule for a sequence of operations. This enables the detailed study of effects of noise correlations on algorithms and periodically driven systems. Moreover, we point out the method's suitability for numerical applications and present the open-source Python software package filter_functions. Amongst other things, it facilitates computing the noise-averaged transfer matrix representation of a unital quantum operation in the presence of universal classical noise for arbitrary control sequences. We apply the presented methods to selected examples.